Method and apparatus for controlling a machine tool

ABSTRACT

A method and apparatus for controlling the operation of a machine tool on a workpiece in which said workpiece and tool are mounted in a machine tool assembly in a position to permit said tool to engage the workpiece to perform work operations thereon and in positions such that a pair of reference points on said workpiece and tool are disposed in spaced relationship. One or both of the workpiece and tool are connected to a first driving member for effecting relative movement between them so that said tool will perform the desired work on the workpiece at their interface. The force exerted on the workpiece by the tool at their interface is detected, and such force is transduced into a response signal. This signal actuates a second driving member, and that second driving member is coupled to one of said workpiece or tool for effecting relative movement therebetween to maintain the reference points on the workpiece and tool at predetermined spaced distances from each other during the performance of the work.

United States Patent Nachtigal METHOD AND APPARATUS FOR CONTROLLING AMACHINE TOOL [76] Inventor: Chester L. Naclltigal, 1310 S. 12th St.,Lafayette, lnd. 47905 22 Filed: Jan. 3, 1972 211 Appl. NOJ 215,200

Related US. Application Data [63] Continuation of Ser. No. 885,686, Dec.17, 1969,

2/1950 Eldridge 3,473,435 10/1969 Tse et al......

[5 7] ABSTRACT A method and apparatus for controlling the operation of amachine tool on a workpiece in which said workpiece and tool are mountedin a machine tool assembly in a position to permit said tool to engagethe workpiece to perform work operations thereon and in positions suchthat a pair of reference points on said workpiece and tool are disposedin spaced relationship. One or both of the workpiece and tool areconnected to a first driving member for effecting relative movementbetween them so that saidtool will perform the desired work on theworkpiece at their interface. The force exerted on the workpiece by thetool at their interface is detected, and such force is transduced into aresponse signal. This signal actuates a second driving member, and thatsecond driving member is coupled to one of said workpiece or tool foreffecting relative movement therebetween to maintain the referencepoints on the workpiece and tool at predetermined spaced distances fromeach other during the performance of the work.

7 Claims, 6 Drawing F lgures CONTROLLER PATENIEI] M18 28 I975 snarl or 2Fig- 1 CONTROLLER INVENTOR CHESTER L. NACHTIGAL BY l m tl E A/ g Mme/iFig.4

ATJ'OR N EYS PATENTEU I828 I973 SHEET 2 UP 2 wuZaFwE TIME muzsba TIMEINVENTOR CHESTER L. NACHTIGAL ATTORNEYS METHOD AND APPARATUS FORCONTROLLING A MACHINE TOOL This application is a continuationapplication of my copending application Ser. No. 885,686, filed Dec. 17,1969, now abandoned.

BACKGROUND OF THE INVENTION In the operation of lathes, millingmachines, drill presses, broaching machines, etc., wherein a machinetool removes material from a workpiece, severe vibra-. tionaloroscillating motion forces can be established. These vibrations can becreated in a variety of different ways. For example, the workpiece maybe mounted in a noncentered position on the machine; it may be out ofround; it may have an irregular surface configuration; it may containdiscontinuous hard or soft areas, etc. In the latter condition, the toolengaging a hard spot will tend to skip an adjacent soft area andvibrational forces between the tool and workpiece will be created. Suchvibrational forces may also be established when the machine is operatingat its own resonant frequency. Vibrational forces can also be created byoutside forces; such as vibrational forces imparted to the machinethrough the floor upon which the machine is mounted. All of thesevibrations create a deviation in the normal path of movement of theworkpiece surface past the tool, that is, a relative movement betweenthe workpiecev and the tool at their interface. This results in the toolimparting nonuniform cutting forces to the workpiece surface moving pastthe tool thereby machining an undesired and nonuniform surface on theworkpiece and resulting in a lack of dimensional precision from oneworkpiece to another. Further, the vibrations, under certaincircumstances, may be amplified to create regenerative chatter betweenthe workpiece and tool and further increase the nonuniformity of themachining operations.

My invention compensates for any such vibrations to permit the tool tomore quickly assume a relative position with respect to the workpiecesuch that the vibrations are suppressed and the static stiffness of themachine tool is increased. This permits an increased rate of productionand results in the reduction of noise levels due to vibrational motion,longer tool life, longer machine life, and increased dimensionalprecision between workpieces.

SUMMARY OF THE INVENTION In accordance with one form of my invention, asit may be employed in a lathe, the workpiece is mounted on the lathe andthe tool housing containing the tool in its tool holder is moved tobring the tool into contact with the surface of the workpiece onwhichthe work is to be performed. A pair of spaced reference points areestablished on or with respect to the workpiece and tool. Such referencepoints may be, for example, the centerline of the workpiece and the toolcutting edge, both of which are disposed at known spaced distances fromthe inner face of the tool housing.

The workpiece is rotated with the tool in bearing engagement with it,and the force exerted by said tool on the workpiece at their interfaceis detected in a continuous manner, as by a strain gage. The detectedforce is converted into a first electrical signal proportional to theinstantaneously occurring cutting force. This first signal is then fedto a controller which acts upon it in a continuous manner and produces asecond signal proportional to the desired tool position. The position ofthe tool is detected and fed back through a transducer to form a thirdelectric signal which is compared with the second signal with theresultant of two signals operating a servo valve controlling theactuation of a servo motor. The servo motor is connected to the toolholder for thus moving the tool with respect to the tool support housingto keep the same relative distances between the workpiece and toolreference points irrespective of the vibratory movements of saidworkpiece.

In the operation of the system, if the workpiece is out of round, thesurface of said workpiece will move toward and away from the tool thuscreating a varying cutting force which in turn causes the centerlinereference point to deviate from its desired location. This change inforce is detected and causes a first signal to be generated and fed tothe controller to create a second signal. Simultaneously, a thirdelectrical signal is generated in response to the tool position. Saidsecond and third signals are compared and their resultant signal is fedthrough the servo motor to the tool causing it to move in the samedirection as the centerline to thereby maintain the predetermineddistance between the tool and the workpiece reference points so thatsaid tool and workpiece centerline will continue to have substantiallythe desired predetermined spaced relationship one to the other. With thetool moving inthe same direction as the vibrating centerline of theworkpiece, the vibrations of the workpiece will be dampened and theworkpiece will more quickly assume a stable state.

BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings illustratethe invention. In such drawings:

FIG. 1 is a diagrammatic showing of the invention as may be practiced ina lathe assembly;

FIG. 2 is a transverse section taken on the line 2'2 of FIG. 1;

FIG. 3 is a diagrammatic showing of the tool servo motor shown inrFIG.l; 1

FIG. 4 is an enlarged diagrammatic showing of th workpiece and tool andindicating their relative positions in a vibratory state;

FIG. 5 is a graphic representation of the relative tool and workpiecereference point locations during one pass of the cutting tool over theworkpiece in the assembly shown in FIG. I; and

FIG. 6 is a graphic representation similar to FIG.'5, but depicting therelative tool and workpiece reference point locations during areciprocating stepwise cutting operation.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT For purposes ofconvenience, the invention is described herein as being employed forcontrolling the operation of a lathe assembly. It .is to be understood,however, that said invention can be employed for controlling theoperation of any machine tool on a workpiece in which portions of saidworkpiece are removed by the tool.

As illustrated in FIG. 4, in such a lathe operation the tool 10 isdisposed in cutting engagement witha workpiece 12 for removing a portionof said workpiece, as at 13, as the workpiece is rotated with respect tosaid tool. Because of various conditions which may exist,

such as for example, the lathe operating at its resonant frequency, anoncentered mounting of the workpiece on the lathe, the workpiecebeingout-of-round, the workpiece having irregular surface con-figurations,the workpiece having discontinuous hard and soft areas, extraneousvibrational forces being imparted to the workpiece through the lathe,etc., said workpiece may vibrate with respect to the tool during thecutting operation. For example, as shown in FIG. 4, the workpiece mayvibrate between the full line position in which its centerline isdisposed at point 14 and the dotted line position in which itscenterline is disposed at point 14'. If compensation for suchvibrational movement is not made in the tool 10, a regenerative chattermay be established, and even in the absence of any such regenerativechatter, the tool will make irregular cuts in the vibrating workpiece asit rotates past said tool. Therefore, my invention compensates for suchvibratory movement of the workpiece by creating a correspondingcontinuously responsive movement of the tool. Thus, for example, whenthe workpiece vibrates into the dotted line position shown in FIG. 4,the tool 10 will also move into its dotted line position represented inFIG. 4 thereby permitting said tool to remove a uniform chip thicknessfrom the vibrating workpiece.

As diagrammatically represented in the drawings, the workpiece 12 ismounted on a lathe l6 and is rotatably driven by a lathe motor 18. Thetool 10 is carried in a tool holder 24 mounted on a tool housing 22. Anysuitable driver 25 may be connected to the housing 22 to advance itinwardly toward the workpiece as the cutting operation proceeds. A pairof reference points are established on the tool and the workpiece.Conveniently, in the illustrated embodiment, the workpiece referencepoint is the centerline 14 of the workpiece, and the tool referencepoint is its cutting edge.

In order to keep the tool 10 in the desired cutting engagement with theworkpiece 12 during the vibratory movements of said workpiece to producea uniform chip thickness as the tool cuts into said workpiece, it isnecessary to establish and maintain a controlled spatial relationshipbetween the reference points on the workpiece and tool. Thus, as shownin FIG. 2, the invention provides a means for continuously andinstanteously changing the value of the dimension X, in response tochanges in the cutting force, said changes in the cutting force being afunction of changes in X,,,. The values of X,,, and X, are the distancesbetween the two reference points and the inner face of the tool housing22.

During the cutting operation, the driver 25 will pro gressively advancethe housing 22 toward the workpiece. This causes X,, to progressivelydecrease, and, in the absence of vibratory movement in the workpiece,X,, will decrease at a substantially straight line rate as indicated byline A in FIG. 5. Since the tool is supported from the housing 22 and ismovable therewith, in the absence of any reciprocating movement beingimparted to the tool to compensate for workpiece vibrations, X, willremain constant as indicated by line B in FIG. 5. Should the workpiecevibrate, however, X, will assume values like those represented by line Cin FIG. 5, and with the tool moving to compensate for such workpiecevibrations, X will assume values like those represented by line D inFIG. 5.

As shown in FIG. 3, the tool holder 24 for tool 10 has a strain gage 26mounted thereon for continuously and instantaneously detecting thecutting force of the tool on the workpiece as the workpiece is rotatedpast said tool. The signals from the'strain gage 26 are transmitted bylines 27 to a transducer 28. The transducer signals are transmitted byline 29 to controller 30 comprising an electrical signal shapingnetwork, and its signals in turn are transmitted by a line 31 to asumming junction 32.

A position measuring transducer 33, conveniently a linear variabledifferential transducer, is connected to the tool holder 24. Thetransducer 33 continuously and instantaneouslyconverts the linearmovement of the tool holder 24, and thus the tool 10, into an electricsignal which is transmitted along line 34 to the side of the junction 32opposite its connection to the controller 30. In this manner, there isprovided a closed loop feedback system for the tool 10. The output ofthe junction 32, which is a signal produced by the difference resultantof the signals received from the transducer 33 and controller 30, is fedby line 36 through an amplifier 37 to a servo valve 40 adapted tocontrol a servo motor 42 having its piston 44 connected to the toolholder 24.

In operation of the system illustrated, the workpiece 12 is mounted onthe lathe, and the tool 10 is moved into a position such that it willremove the desired chip thickness from said workpiece as it is rotatedpast the toolJThus, the locations of the reference points, asrepresented by the workpiece centerline l4 and the tool cutting edge,are established so that there is an established relationship between thedimensions X, and X,,,. With the tool disposed in the desired cuttingengagement with the workpiece, the cutting force of said tool at itsinterface with the workpiece 12 is continuously and instantaneouslydetected by strain gage 26, which force is translated through thetransducer 28 and controller 30 as a reference voltage imposed upon thesumming junction 32. From knowledge of the machine characteristics thecontroller is designed or adjusted to respond to the cutting forcesignal generated by the strain gage 26 so as to produce a signal whichis proportional to X, and which also serves as a reference for the toolposition X,. Simultaneously with the development of the strain gagesignal, the position of the tool (X,) is detected, and a signalcorresponding to that position is fed from the transducer 33 to thejunction 32.

In the absence of any vibration of the workpiece 12 during its rotationpast the tool 10, X, will decrease at a predetermined constant rate withrespect to X, as housing 22 is advanced toward the workpiece as thecutting operation proceeds as shown by line A in FIG. 5. Also, thecutting force will remain constant. However, should the workpiece 12assume a vibrating motion during its rotation, thus causing it to movetoward and away from the tool 10 as represented by the dotted and fulllines shown in FIG. 4 and line C in FIG. 5, the cutting force exerted bythe tool 10 will change causing the strain gage 26, transducer 28, andcontroller 30 to change the voltage imposed upon the junction 32. Thiscreates an imbalance between the voltages imposed upon the junction 32by the controller 30 and transducer 33 whereby a new output resultantvoltage of the junction 32 is transmitted through the amplifier 37 tothe servo valve 40 causing it to actuate the servo motor 42 to move thetool 10 in a direction to re-establish a balance between the voltagesimposed upon the junction 32.

Thus, for example, should the workpiece vibrate in a direction to moveits centerline away from the tool- 10 and thus increase X,, with respectto X the cutting force of tool will be changed. This difference in thecutting force is detected by the strain gage 26 so that the signaltransmitted by the gage through the transducer 28 to the controller 30is changed, and said controller will impose a different voltage on thejunction 32 with respect to the voltage imposed on said junction by thetransducer 33, whereupon the valve 40 will actuate the motor 42 to drivethe tool 10 in the same direction as the centerline 14 is moved awayfrom said tool. The movement of the tool 10 is detected by thetransducer 33 to thus change the voltage that it imposes upon thejunction 32 thereby bringing the voltages imposed by the controller andtransducer on junction 32 into balance. Further, by measuring ordetecting the position of the tool with respect to its mountingstructure, the movement of the piston 44 can be very accuratelycon-trolled to permit the tool to perform very precise machiningoperations. Thus, as shown in FIG. 5, the deviations in X,,, due to thevibrating workpiece are shown by line C, and corresponding in phasedeviations in X, as shown by line D are produced to compensate for suchworkpiece vibrations.

As will be seen, such reciprocal movement of the tool 10 in response tothe vibratory movement of the workpiece 12 maintains the distances X,and X in the proper relationship as the workpiece is rotated past thetool although X will decrease with respect to X, at a predetermined rateas the tool advances into the workpiece during its successiverevolutions of the workpiece. By moving the tool in response to, andsubstantially simultaneously with, the vibrating workpiece 12, thevibrations of said workpiece are dampenedboth in amplitude and duration.Further, such vibratory compensating movement of the tool will causesaid tool to effect a substantially uniform chip thickness removal fromthe workpiece and thereby create dimensional precision betweenworkpieces.

Because of the machine and workpiece characeristics in the latheassembly shown in FIGS. 1 and 2, it is the workpiece that vibrates withrespect to the tool. And because of the type of machining operationinvolved, there is a substantially continuous cutting operation wherebyX,, decreases in a continuous manner during the machining operation. Ina planing operation the situation is somewhat different. There, becauseof the machine characteristics, the workpiece is fixed and any vibratorymovements occur in the tool support. Any such vibratory movements will,however, still create deviations in X,, which necessitate correspondingdeviations in X, if a uniform cutting force is to be maintained.Further, in the operation of such assemblies, the cutting operationsproceed in a stepwise manner as the tool or-workpiece are transversedback and forth one with respect to the other. Thus, FIG. 6 shows thecurves for X,, and X, in such a planing operation. As shown by Line E,in a static or nonvibrating state, X, decreases in a stepwise manner asthe machining proceeds while X, remains constant as shown by line F.However, if a vibratory movement occurs, X, will deviate in the mannershown by line G. A corresponding deviation is established in X, as shownby line H in the manner previously described so as to maintain asubstantially uniform cutting force.

While the invention has been described as employing an electrical signaland servo motor assembly to efi'ect tool movement in response tovibratory movement of the workpiece, it is to be understood, of course,that any desired response and driving system can be employed to effectthe desired tool movement in response to the vibratory movement of theworkpiece. Further, it may also be desired to sense the cutting forceand effect a corresponding tool movement on a stepwise basis instead ofa continuous basis.

I claim:

1. An apparatus for controlling a cutting tool in which a workpiece andsaid cutting tool are mounted in a machine tool assembly and one of saidworkpiece and cutting tool is moved with respect to the other to causesaid cutting tool to cut into said workpiece, comprising tirst meansoperatively connected to said cutting tool for measuring its cuttingforce on the workpiece, transducer means coupled to said first means forproducing a first electric signal, a signal shaping network receivingsaid first electric signal and converting it into a second electricsignal related to the desired position of said cutting tool, secondmeans operatively connected to said cutting tool for detecting theactual position of said tool and converting such actual position into athird electric signal, a summing junction adapted to receive and combinesaid second and third electric signals into a fourth electric signal,and a driver operatively connected to said tool and actuated by saidfourth electric signal to move said cutting tool with respect to saidworkpiece to maintain said workpiece and cutting tool in predeterminedspatial relationships during the cutting operation irrespective of anyvibrating movements of said workpiece or machine tool assembly.

2. The invention as set forth in claim 1 in which said first meanscomprises a strain gageoperatively connected to said cutting tool, saidtransducing means comprises a transducer coupled to said strain gage andsaid signal shaping network, and said secondmeans comprises a secondtransducer operatively connected to said cutting tool.

3. An apparatus for controlling a cutting tool in which a workpiece andsaid cutting tool are mounted in a machine tool assembly and one of saidworkpiece and cutting tool is moved with respect to the other to causesaid cutting tool to cut into said workpiece, comprising a strain gageoperatively connected to said cutting tool for measuring its cuttingforce, a transducer coupled to said strain gage and a signal shapingnetwork, said transducer and signal shaping network producing a firstelectrical signal adapted to serve as a reference signal for the desiredpositionof said tool, a second transducer operatively connected to saidtool adapted to produce a second electrical signal in response to theposition of said tool, a summing junction connected to said signalshaping network and second transducer for combining said first andsecond electrical signals, and a servo motor operatively connected tosaid tool and controlled by a servo valve actuated by the signal fromsaid summing junction, said servo motor moving said tool with respect tosaid workpiece to maintain said cuttingtool and workpiece in prede--terrnined spatial relationships during the cutting operationirrespective of any vibratory movements of said workpiece or machinetool assembly.

4. An apparatus for controlling a cutting tool in which a workpiece andsaid cutting tool are mounted in a machine tool assembly and one of saidworkpiece and cutting tool is moved with respect to the other to causesaid cutting tool to cut into said workpiece, comprising first meansoperatively connected to said tool for measuring its cutting force onthe workpiece, means coupled to said first means producing a firstelectric signal adapted to serve as a reference signal for the desiredposition of said cutting tool, second means operatively connected tosaid cutting tool for detecting the actual position of said cutting tooland converting said position into a second electric signal, means forcombining said first and second signals to produce a resultant signal,and a driver operatively connected to said tool and actuated by saidresultant signal to move said tool with respect to the workpiece tomaintain said cutting tool and workpiece in predetermined spatialrelationships irrespective of any vibratory movements of said workpieceor machine tool assembly.

5. An apparatus for controlling a cutting tool in which a workpiece andsaid cutting tool are mounted in a machine tool assembly and one of saidworkpiece and cutting tool is moved with respect to the other to causesaid cutting tool to cut into said workpiece, comprising first sensingmeans operatively connected to the cutting tool for measuring itscutting force on the workpiece, means coupled to said first sensingmeans for converting the measurement of said cutting force into a firstelectrical signal related to the desired position of said cutting tool,second sensing means operatively connected to the cutting tool fordetecting the actual position of said cutting tool and converting suchactual position into a second electrical signal, means for combiningsaid first and second electrical signals into a resultant signal, and adriver operatively connected to said cutting tool and actuated by saidresultant signal to move said cutting tool with respect to saidworkpiece to maintain said workpiece and cutting tool in predeterminedspatial relationships during the cutting operation irrespective of anyvibrating movements of said workpiece or machine tool assembly.

6. A method of controlling the operation of a cutting tool on aworkpiece, comprising the steps of mounting said workpiece in a machinetool assembly in a position to permit said cutting tool to engage saidworkpiece and with a spaced distance between a pair of reference pointson said cutting tool and workpiece, coupling at least one of saidworkpiece and cutting tool to a first driving member for effecting afirst relative movement therebetween whereby said cutting tool willperform the desired work on said workpiece at their interface,continuously detecting the force exerted on the workpiece by the cuttingtool at their interface, converting said force into a first responsesignal related to the desired position of said tool, continuouslydetecting the position of the cutting tool and converting said positioninto a second response signal, combining said first and second signalsand imposing the resultant signal on a second driving member to actuatesaid second driving member, said first and second signals beingcontinuously and instantaneously generated and combined to provide acontinuous and instantaneous resultant signal, and coupling said seconddriving member to one of said workpiece or cutting tool for effecting asecond relative movement therebetween to maintain said reference pointsat predetermined spaced distances from each other during said work.

7. A method of controlling the operation of a cutting tool on aworkpiece, comprising the steps of mounting said workpiece and cuttingtool in a machine tool assembly in a position to permit said cuttingtool to exert a cutting force on said workpiece at their interface,coupling at least one of said workpiece and cutting tool to a firstdriving member for effecting a first relative movement therebetweenwhereby said cutting tool will perform the desired work on saidworkpiece at their interface, continuously detecting said cutting forceand converting it into a first electric signal related to the desiredposition of the cutting tool, continuously detecting and converting theposition of said cutting tool into a second electric signal, continouslycombining said first and second signals to produce a third electricalsignal, and imposing said third electrical signal on a second drivingmember to actuate said second driving member, and coupling said seconddriving member to one of said workpiece or cutting tool for effecting asecond relative movement therebetween to maintain predetermined spatialrelationships between said workpiece and cutting tool of any vibratingmovements of said workpiece or assembly.

l 1' t k

1. An apparatus for controlling a cutting tool in which a workpiece andsaid cutting tool are mounted in a machine tool assembly and one of saidworkpiece and cutting tool is moved with respect to the other to causesaid cutting tool to cut into said workpiece, comprising first meansoperatively connected to said cutting tool for measuring its cuttingforce on the workpiece, transducer means coupled to said first means forproducing a first electric signal, a signal shaping network receivingsaid first electric signal and converting it into a second electricsignal related to the desired position of said cutting toOl, secondmeans operatively connected to said cutting tool for detecting theactual position of said tool and converting such actual position into athird electric signal, a summing junction adapted to receive and combinesaid second and third electric signals into a fourth electric signal,and a driver operatively connected to said tool and actuated by saidfourth electric signal to move said cutting tool with respect to saidworkpiece to maintain said workpiece and cutting tool in predeterminedspatial relationships during the cutting operation irrespective of anyvibrating movements of said workpiece or machine tool assembly.
 2. Theinvention as set forth in claim 1 in which said first means comprises astrain gage operatively connected to said cutting tool, said transducingmeans comprises a transducer coupled to said strain gage and said signalshaping network, and said second means comprises a second transduceroperatively connected to said cutting tool.
 3. An apparatus forcontrolling a cutting tool in which a workpiece and said cutting toolare mounted in a machine tool assembly and one of said workpiece andcutting tool is moved with respect to the other to cause said cuttingtool to cut into said workpiece, comprising a strain gage operativelyconnected to said cutting tool for measuring its cutting force, atransducer coupled to said strain gage and a signal shaping network,said transducer and signal shaping network producing a first electricalsignal adapted to serve as a reference signal for the desired positionof said tool, a second transducer operatively connected to said tooladapted to produce a second electrical signal in response to theposition of said tool, a summing junction connected to said signalshaping network and second transducer for combining said first andsecond electrical signals, and a servo motor operatively connected tosaid tool and controlled by a servo valve actuated by the signal fromsaid summing junction, said servo motor moving said tool with respect tosaid workpiece to maintain said cutting tool and workpiece inpredetermined spatial relationships during the cutting operationirrespective of any vibratory movements of said workpiece or machinetool assembly.
 4. An apparatus for controlling a cutting tool in which aworkpiece and said cutting tool are mounted in a machine tool assemblyand one of said workpiece and cutting tool is moved with respect to theother to cause said cutting tool to cut into said workpiece, comprisingfirst means operatively connected to said tool for measuring its cuttingforce on the workpiece, means coupled to said first means producing afirst electric signal adapted to serve as a reference signal for thedesired position of said cutting tool, second means operativelyconnected to said cutting tool for detecting the actual position of saidcutting tool and converting said position into a second electric signal,means for combining said first and second signals to produce a resultantsignal, and a driver operatively connected to said tool and actuated bysaid resultant signal to move said tool with respect to the workpiece tomaintain said cutting tool and workpiece in predetermined spatialrelationships irrespective of any vibratory movements of said workpieceor machine tool assembly.
 5. An apparatus for controlling a cutting toolin which a workpiece and said cutting tool are mounted in a machine toolassembly and one of said workpiece and cutting tool is moved withrespect to the other to cause said cutting tool to cut into saidworkpiece, comprising first sensing means operatively connected to thecutting tool for measuring its cutting force on the work-piece, meanscoupled to said first sensing means for converting the measurement ofsaid cutting force into a first electrical signal related to the desiredposition of said cutting tool, second sensing means operativelyconnected to the cutting tool for detecting the actual position of saidcutting tool and converting such actual posiTion into a secondelectrical signal, means for combining said first and second electricalsignals into a resultant signal, and a driver operatively connected tosaid cutting tool and actuated by said resultant signal to move saidcutting tool with respect to said workpiece to maintain said workpieceand cutting tool in predetermined spatial relationships during thecutting operation irrespective of any vibrating movements of saidworkpiece or machine tool assembly.
 6. A method of controlling theoperation of a cutting tool on a workpiece, comprising the steps ofmounting said workpiece in a machine tool assembly in a position topermit said cutting tool to engage said workpiece and with a spaceddistance between a pair of reference points on said cutting tool andworkpiece, coupling at least one of said workpiece and cutting tool to afirst driving member for effecting a first relative movementtherebetween whereby said cutting tool will perform the desired work onsaid workpiece at their interface, continuously detecting the forceexerted on the workpiece by the cutting tool at their interface,converting said force into a first response signal related to thedesired position of said tool, continuously detecting the position ofthe cutting tool and converting said position into a second responsesignal, combining said first and second signals and imposing theresultant signal on a second driving member to actuate said seconddriving member, said first and second signals being continuously andinstantaneously generated and combined to provide a continuous andinstantaneous resultant signal, and coupling said second driving memberto one of said workpiece or cutting tool for effecting a second relativemovement therebetween to maintain said reference points at predeterminedspaced distances from each other during said work.
 7. A method ofcontrolling the operation of a cutting tool on a workpiece, comprisingthe steps of mounting said workpiece and cutting tool in a machine toolassembly in a position to permit said cutting tool to exert a cuttingforce on said workpiece at their interface, coupling at least one ofsaid workpiece and cutting tool to a first driving member for effectinga first relative movement therebetween whereby said cutting tool willperform the desired work on said workpiece at their interface,continuously detecting said cutting force and converting it into a firstelectric signal related to the desired position of the cutting tool,continuously detecting and converting the position of said cutting toolinto a second electric signal, continously combining said first andsecond signals to produce a third electrical signal, and imposing saidthird electrical signal on a second driving member to actuate saidsecond driving member, and coupling said second driving member to one ofsaid workpiece or cutting tool for effecting a second relative movementtherebetween to maintain predetermined spatial relationships betweensaid workpiece and cutting tool of any vibrating movements of saidworkpiece or assembly.